1. Field of the Invention
The invention relates in general to a method of signal compression, and more particularly, to a method of signal compression in multi-domains based on wavelet packet transform.
2. Description of the Related Art
Wavelet transform or wavelet packet transform has been proved to be a very useful technique for time-varying signal analysis and process, especially in image compression and audio compression. The wavelet transform is developed based on Fourier analysis. Due to a much better time-frequency resolution compared to the Fourier transform, a better localization property in both time domain and frequency domain is obtained. Therefore, the wavelet transform and the wavelet packet transform have great effects on signal analysis and measurement, image process, speech process, and automatic control. By employing wavelet transform or wavelet packet transform for signal process, for example, for speech compression, a wide applicability, a high quality of speech, and a good robustness are obtained. Furthermore, this technique can be introduced into a low bit rate encoding, of which the research is rarely seen in literature.
Considering a discrete orthogonal wavelet transform, assuming that there is a wavelet function .PSI.(x). This wavelet function .PSI.(x) has to meet certain requirements. By using this wavelet function .PSI.(x) as a prototype, through dilation and translation, a function sequence is obtained as: EQU {.PSI..sub.j,k =2.sup.j/2 .PSI.(2.sup.-j x-k).vertline.j,k.di-elect cons.Z}
where j, k are scale index and shift index, respectively.
This function sequence thus constructs a normalized orthogonal base in space of L(R.sup.2). For an arbitrary function f(x) in space L(R.sup.2), a wavelet transform is as: ##EQU1## The inverse transform is defined as: ##EQU2##
By employing the wavelet transform, with a certain time and frequency resolution, a signal can be decomposed into an approximate component and a detailed component, that is, a low-pass component and a high-pass component, respectively. The decomposition is shown as FIG. 1. As shown in the figure, an input function f(x) is decomposed into a first low-pass component w.sub.1.sup.H and a first high-pass component w.sub.1.sup.G. The low-pass component w.sub.1.sup.H is further decomposed into a second pair of components, which comprises a second low-pass component w.sub.2.sup.H and a second high-pass component w.sub.2.sup.G, whereas the first high-pass component w.sub.1.sup.G remains as ever. Again, the second low-pass component w.sub.2.sup.H is decomposed into a third pair of components, w.sub.3.sup.H and w.sub.3.sup.G. By iterating the same process of decomposition, a wavelet transform is performed.
Wavelet packet transform is a further development of the wavelet transform. The wavelet packet transform is shown as FIG. 2. The wavelet packet transform has been adapted in speech encoding research. At first, properties of wavelet packet transform are applied for parameter extract, for example, pitch extract and envelope extract, in speech encoding. Later on, by combining wavelet packet transform, entropy encoding technique, and vector quantization technique, some algorithms of speech encoding are developed. For example, Tewfik et. al. employs the wavelet packet transform to perform a high quality encoding research of wide band audio. By wavelet packet transform, the critical band decomposition of an audio signal segment is identified. Averbuch et. al. develops an algorithm by combining the wavelet pack transform and the vector quantization technique.
An algorithm of speech encoding based on wavelet packet transform has been presented in literature. A wavelet packet transform with a fixed decomposition level is performed for an input speech signal segment. That is, the signal is transformed into a fixed time-frequency space. In the space, the time-frequency resolution is approximately the same as that of hearing system of human beings. Therefore, the transform is performed in both time and frequency domains, not only in frequency domain.
An encoding process for a method of speech compression is shown as FIG. 3. It has to be noted that the input signal is variable in a wide range, therefore, it is difficult to perform an effective decomposition by using the wavelet packet transform in a fixed domain. In addition, through wavelet packet transform, a signal band is dyadic (binary tree) decomposed flexibly. Theoretically, the performance of a best wavelet packet transform is achieved by defining a cost function, such as an entropy function or an energy function, first. Using the cost function as a standard to select how to perform a wavelet packet decomposition under a binary tree. The result of decomposition causes the function to be a maximum or a minimum. It is thus advantageous for process. However, in practice use, the cost of this method is too much to perform no matter under the consideration of time or complexity, especially in the application of speech encoding.